Which of the following numbers is a factor of 49? ${2,5,7,9,14}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $49$ by each of our answer choices. $49 \div 2 = 24\text{ R }1$ $49 \div 5 = 9\text{ R }4$ $49 \div 7 = 7$ $49 \div 9 = 5\text{ R }4$ $49 \div 14 = 3\text{ R }7$ The only answer choice that divides into $49$ with no remainder is $7$ $ 7$ $7$ $49$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $49$ $49 = 7\times7 7 = 7$ Therefore the only factor of $49$ out of our choices is $7$. We can say that $49$ is divisible by $7$.